Viscoelastic Models for Ligaments and Tendons

1994 ◽  
Vol 47 (6S) ◽  
pp. S282-S286 ◽  
Author(s):  
S. L.-Y. Woo ◽  
G. A. Johnson ◽  
R. E. Levine ◽  
K. R. Rajagopal
Keyword(s):  
Constitutive Modeling ◽  
Finite Strain ◽  
Experimental Studies ◽  
Viscoelastic Behavior ◽  
Microstructural Change ◽  
Viscoelastic Models ◽  
Dependent Behavior ◽  
Recent Approach ◽  
Single Integral ◽  
Strain Model

Ligaments and tendons serve a variety of important functions in the human body. Many experimental studies have focused on understanding their mechanical behavior, mathematical modeling has also contributed important information. This paper presents a brief review of viscoelastic models that have been proposed to describe the nonlinear and time-dependent behavior of ligaments and tendons. Specific attention is devoted to quasi-linear viscoelasticity (QLV) and to our most recent approach, the single integral finite strain model (SIFS) which incorporates constitutive modeling of microstructural change. An example is given in which the SIFS model is used to describe the viscoelastic behavior of a human patellar tendon.

Mathematical Modeling of Ligaments and Tendons

1993 ◽  
Vol 115 (4B) ◽  
pp. 468-473 ◽  
Author(s):  
S. L.-Y. Woo ◽  
G. A. Johnson ◽  
B. A. Smith
Keyword(s):  
Mathematical Modeling ◽  
Finite Strain ◽  
Mechanical Response ◽  
Time Dependent ◽  
Experimental Investigations ◽  
Display Time ◽  
Viscoelastic Models ◽  
The Past ◽  
Dependent Behavior ◽  
Single Integral

Ligaments and tendons serve a variety of important functions in maintaining the structure of the human body. Although abundant literature exists describing experimental investigations of these tissues, mathematical modeling of ligaments and tendons also contributes significantly to understanding their behavior. This paper presents a survey of developments in mathematical modeling of ligaments and tendons over the past 20 years. Mathematical descriptions of ligaments and tendons are identified as either elastic or viscoelastic, and are discussed in chronological order. Elastic models assume that ligaments and tendons do not display time dependent behavior and thus, they focus on describing the nonlinear aspects of their mechanical response. On the other hand, viscoelastic models incorporate time dependent effects into their mathematical description. In particular, two viscoelastic models are discussed in detail; quasi-linear viscoelasticity (QLV), which has been widely used in the past 20 years, and the recently proposed single integral finite strain (SIFS) model.

A Single Integral Finite Strain Viscoelastic Model of Ligaments and Tendons

1996 ◽  
Vol 118 (2) ◽  
pp. 221-226 ◽  
Author(s):  
G. A. Johnson ◽  
G. A. Livesay ◽  
S. L-Y. Woo ◽  
K. R. Rajagopal
Keyword(s):  
Finite Strain ◽  
Viscoelastic Model ◽  
Three Dimensional ◽  
Uniaxial Extension ◽  
Viscoelastic Behavior ◽  
Nonlinear Behavior ◽  
Biological Tissues ◽  
Model Parameters ◽  
Three Dimensional Model ◽  
Single Integral

A general continuum model for the nonlinear viscoelastic behavior of soft biological tissues was formulated. This single integral finite strain (SIFS) model describes finite deformation of a nonlinearly viscoelastic material within the context of a three-dimensional model. The specific form describing uniaxial extension was obtained, and the idea of conversion from one material to another (at a microscopic level) was then introduced to model the nonlinear behavior of ligaments and tendons. Conversion allowed different constitutive equations to be used for describing a single ligament or tendon at different strain levels. The model was applied to data from uniaxial extension of younger and older human patellar tendons and canine medial collateral ligaments. Model parameters were determined from curve-fitting stress-strain and stress-relaxation data and used to predict the time-dependent stress generated by cyclic extensions.

Identification of Nonlinear Viscoelastic Models of Flexible Polyurethane Foam From Uniaxial Compression Data

2016 ◽  
Vol 138 (2) ◽  
Author(s):  
Yousof Azizi ◽  
Patricia Davies ◽  
Anil K. Bajaj
Keyword(s):  
Uniaxial Compression ◽  
Viscoelastic Model ◽  
Viscoelastic Behavior ◽  
Model Parameters ◽  
Viscoelastic Models ◽  
Nonlinear Viscoelastic ◽  
Compression Data ◽  
Computationally Intensive ◽  
Nonlinear Viscoelastic Model ◽  
Flexible Polyurethane

Flexible polyethylene foam is used in many engineering applications. It exhibits nonlinear and viscoelastic behavior which makes it difficult to model. To date, several models have been developed to characterize the complex behavior of foams. These attempts include the computationally intensive microstructural models to continuum models that capture the macroscale behavior of the foam materials. In this research, a nonlinear viscoelastic model, which is an extension to previously developed models, is proposed and its ability to capture foam response in uniaxial compression is investigated. It is hypothesized that total stress can be decomposed into the sum of a nonlinear elastic component, modeled by a higher-order polynomial, and a nonlinear hereditary type viscoelastic component. System identification procedures were developed to estimate the model parameters using uniaxial cyclic compression data from experiments conducted at six different rates. The estimated model parameters for individual tests were used to develop a model with parameters that are a function of strain rates. The parameter estimation technique was modified to also develop a comprehensive model which captures the uniaxial behavior of all six tests. The performance of this model was compared to that of other nonlinear viscoelastic models.

Constitutive modeling of strain-dependent bond breaking and healing kinetics of chemical polyampholyte (PA) gel

Soft Matter ◽  
2021 ◽  
Vol 17 (15) ◽  
pp. 4161-4169
Author(s):  
Sairam Pamulaparthi Venkata ◽  
Kunpeng Cui ◽  
Jingyi Guo ◽  
Alan T. Zehnder ◽  
Jian Ping Gong ◽  
...  
Keyword(s):  
Constitutive Model ◽  
Uniaxial Tension ◽  
Constitutive Modeling ◽  
Finite Strain ◽  
Bond Breaking ◽  
Nonlinear Viscoelastic ◽  
Viscoelastic Constitutive Model ◽  
Kinetics Of ◽  
Strain Dependent

A finite strain nonlinear viscoelastic constitutive model is used to study the uniaxial tension behaviour of a chemical polyampholyte (PA) gel.

A thermo-mechanically coupled finite strain model considering inelastic heat generation

2015 ◽  
Vol 28 (4) ◽  
pp. 993-1007 ◽  
Author(s):  
Vladimir Dunić ◽  
Nenad Busarac ◽  
Vukašin Slavković ◽  
Bojana Rosić ◽  
Rainer Niekamp ◽  
...  
Keyword(s):  
Heat Generation ◽  
Finite Strain ◽  
Strain Model

A finite strain model of combined viscoplasticity and rate-independent plasticity without a yield surface

2013 ◽  
Vol 224 (9) ◽  
pp. 2107-2125 ◽  
Author(s):  
V. P. Panoskaltsis ◽  
L. C. Polymenakos ◽  
D. Soldatos
Keyword(s):  
Yield Surface ◽  
Finite Strain ◽  
Strain Model

Constitutive Modeling of Asphalt Bound Granular Materials: Applications to Sand Asphalt

2002 ◽  
Author(s):  
J. Murali Krishnan ◽  
K. R. Rajagopal
Keyword(s):  
Granular Materials ◽  
Asphalt Concrete ◽  
Constitutive Modeling ◽  
Hot Mix Asphalt ◽  
Constitutive Relations ◽  
Experimental Studies ◽  
Compressive Creep ◽  
Multiple Natural Configurations

In the earlier paper, we developed constitutive relations for two kinds of hot mix asphalt, viz., asphalt concrete and sand asphalt using the framework of materials with multiple natural configurations. In the present paper, we apply the framework that we developed for sand asphalt to study compressive creep experiments. Experimental studies of Wood and Goetz (1959) are used to compare with the predictions of the model.

scholarly journals Constitutive Modeling of Time-Dependent Response of Human Plantar Aponeurosis

2014 ◽  
Vol 2014 ◽  
pp. 1-8 ◽  
Author(s):  
P. G. Pavan ◽  
P. Pachera ◽  
C. Stecco ◽  
A. N. Natali
Keyword(s):  
Experimental Data ◽  
Stress Relaxation ◽  
Constitutive Model ◽  
Transverse Isotropy ◽  
Model Fitting ◽  
Viscoelastic Behavior ◽  
Time Dependent ◽  
Plantar Aponeurosis ◽  
Structural Conformation ◽  
Dependent Behavior

The attention is focused on the viscoelastic behavior of human plantar aponeurosis tissue. At this purpose, stress relaxation tests were developed on samples taken from the plantar aponeurosis of frozen adult donors with age ranging from 67 to 78 years, imposing three levels of strain in the physiological range (4%, 6%, and 8%) and observing stress decay for 240 s. A viscohyperelastic fiber-reinforced constitutive model with transverse isotropy was assumed to describe the time-dependent behavior of the aponeurotic tissue. This model is consistent with the structural conformation of the tissue where collagen fibers are mainly aligned with the proximal-distal direction. Constitutive model fitting to experimental data was made by implementing a stochastic-deterministic procedure. The stress relaxation was found close to 40%, independently of the level of strain applied. The agreement between experimental data and numerical results confirms the suitability of the constitutive model to describe the viscoelastic behaviour of the plantar aponeurosis.

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